A) \[\frac{5W}{6}\]
B) \[\frac{W}{6}\]
C) \[\frac{3W}{2}\]
D) \[\frac{4W}{9}\]
Correct Answer: D
Solution :
Weight on earth is \[\omega =mg=\frac{GmM}{{{R}^{2}}}\] ...(i) \[\because \] \[g=\frac{GM}{{{R}^{2}}}\] Now, at a height h above the earth surface, the value of g will become \[g=\frac{GM}{{{(R+h)}^{2}}}\] Now, weight of the body at this height is given by \[\omega =mg=\frac{GnM}{{{(R+h)}^{2}}}\] (ii) Now, dividing equation (ii) by (i) we obtam \[\frac{\omega }{\omega }=\frac{R}{R+h}\] \[h=\frac{R}{2}\] given, \[\omega =\omega \frac{{{R}^{2}}}{{{\left( R+\frac{R}{2} \right)}^{2}}}=\frac{4\omega }{9}\]
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